What is log_{10}(x)-5log_{10}(y)+8log_{10}(z) ?

The solution to log_{10}(x)-5log_{10}(y)+8log_{10}(z) is log_{10}((xz^8)/(y^5))

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simplify log_{10}(x)-5log_{10}(y)+8log_{10}(z)

simplify

lo g_{10} (x) - 5 lo g_{10} (y) + 8 lo g_{10} (z)

lo g_{10} (\frac{x z ^{8}}{y ^{5}})

Solution steps

lo g_{10} (x) - 5 lo g_{10} (y) + 8 lo g_{10} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

5 lo g_{10} (y) = lo g_{10} (y^{5})

= lo g_{10} (x) - lo g_{10} (y^{5}) + 8 lo g_{10} (z)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (x) - lo g_{10} (y^{5}) = lo g_{10} (\frac{x}{y ^{5}})

= lo g_{10} (\frac{x}{y ^{5}}) + 8 lo g_{10} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

8 lo g_{10} (z) = lo g_{10} (z^{8})

= lo g_{10} (\frac{x}{y ^{5}}) + lo g_{10} (z^{8})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (\frac{x}{y ^{5}}) + lo g_{10} (z^{8}) = lo g_{10} (\frac{x}{y ^{5}} z^{8})

= lo g_{10} (\frac{x}{y ^{5}} z^{8})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{10} (\frac{x z ^{8}}{y ^{5}})

lo g_{7} (6) + lo g_{7} (3) - lo g_{7} (2)

- 7 ln (x) - 8 ln (y) - 3 ln (z)

ln (\frac{2}{15})

- 3 (\frac{1}{2} ln (2^{2} - 9) - \frac{1}{2} ln (- 2^{2} - 9))

lo g_{b} (\frac{1}{10}) + lo g_{b} (30)

What is log_{10}(x)-5log_{10}(y)+8log_{10}(z) ?
The solution to log_{10}(x)-5log_{10}(y)+8log_{10}(z) is log_{10}((xz^8)/(y^5))